One-relator quotients and free products of cyclics

Author:

Fine Benjamin,Howie James,Rosenberger Gerhard

Abstract

It is proven that the Freiheitssatz holds for all one-relator products of cyclic groups if the relator is cyclically reduced and a proper power. The method of proof involves representing such groups in PS L 2 ( C ) {\text {PS}}{{\text {L}}_2}({\mathbf {C}}) and is a refinement of a technique of Baumslag, Morgan and Shalen. The technique allows the extension of the Freiheitssatz result to many additional one-relator products.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. Generalized triangle groups;Baumslag, Gilbert;Math. Proc. Cambridge Philos. Soc.,1987

2. On one-relator groups having elements of finite order;Fischer, J.;Proc. Amer. Math. Soc.,1972

3. One-relator products of groups;Howie, James,1986

4. Cohomology of one-relator products of locally indicable groups;Howie, James;J. London Math. Soc. (2),1984

5. Elements of finite order in groups with a single defining relation;Karrass, A.;Comm. Pure Appl. Math.,1960

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